Learn Dutch: Ik kook de soep in een pannetje. - I cook the soup in a little pan.

The base word is pan. Because it has a single short vowel 'a' followed by a single consonant 'n', we must double the 'n' and add -etje. This keeps the 'a' sounding short. If we just added -tje, the Dutch spelling rules would make the vowel sound long.

Diminutives are always het words, so why do we use een before pannetje?

You are right that all diminutives take het for "the" (so "the little pan" is het pannetje). However, the indefinite article for "a" or "an" is always een in Dutch, regardless of whether the noun is a de word or a het word.

Does the verb koken mean "to cook" or "to boil"?

It means both! In Dutch, koken is used both for preparing food (like cooking soup) and for liquids reaching their boiling point (like boiling water). Context tells you which meaning fits best.

Why does de soep come before the location in een pannetje?

In a standard Dutch sentence, the direct object (de soep) usually comes directly after the main verb. Prepositional phrases that describe a location or place (like in een pannetje) are placed later in the sentence.